The prior art is replete with various remote keyless entry systems typically used for remotely actuating door locks in vehicles or opening garage doors. Typically, these systems are comprised of a remote transmitter that uses an RF or IR signal to transmit a multibit message comprised of a command code and an identification code (ID), e.g., an authorization code, and a receiver that responds to this command code when its ID matches the transmitted ID. Such systems are susceptible to pirating apparatus, i.e., scanners, that rapidly scan through all available IDs until a receiver grants them access. In response, entry systems have been designed to penalize wrong transmissions by not accepting additional transmissions for a time period. Other pirating apparatus, i.e., grabbers, capture, i.e., receive and store, the transmitted signal and then later retransmit this captured signal to obtain unauthorized access to a vehicle or garage. In response, entry systems have been designed in which an algorithm in the transmitter causes its authorization code to change, i.e., hop, each transmission. The receiver then uses an identical algorithm to authenticate each received authorization code.